MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.013 Electromagnetics and Applications
Problem Set 6 (five problems)
Suggested Reading:
Course notes, Sections 7.1.1-7.1.2, 7.2.1-7.2.2, 8.1, 8.3.1
Problem 6.
3.012 STATISTICAL MECHANICS practice problems
Issued: 12.14.05
3.012
Fall 2005
1. Engel and Reid, P31.12.
2. Engel and Reid, P31.13.
3. Engel and Reid, P31.19.
4. Engel and Reid, P31.20.
5. Engel and Reid, P33.3.
6. A system of a molecule in a magnetic fi
of them with its corresponding eigenfunction. Can you describe what is happening for E
lesser than zero ? Do we still have eigenstates ? What happens when E is not an eigenvalue
? Note that the applet starts its numerical integration from left to the righ
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Electrical Engineering and Computer Science
6.013 Electromagnetics and Applications
Problem Set 7 (five problems)
Suggested Reading:
Course notes:
Sections 7.2.3, 7.3.17.3.2, 8.3.1, 3.5
Problem 7.1
A los
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DepartmentofElectricalEngineeringandComputerScience
6.013 Electromagnetics and Applications
Problem Set 9 (four problems)
Suggested Reading:
Coursenotes: Sections 9.3.12;9.4;10.3.12,10.3.5;and
11.4.111.4.2
Problem 9.1
m1
l
m2
r
O
(t)K
Izz
O
rod
IG =
1
m1 l2
12
disk
IG =
1
m2 r2
2
O
"
# "
#
2
2
l
1
l
1
2
2
IO = m1
+ m1 l + m 2
+ m2 r
2
12
2
2
1
IO = m1 l2 + m2
3
l2
r2
+
2
4
~
H O = IO ! = I O k
X
(t)
1
m 1 l 2 + m2
3
~O =
~
dH O
dt
l
(m1 + m2 )g sin = I0
2
l2
r2
+
Problem Set 9 Solutions
Problem 9.1
a)
The waveguide will propagate only one mode in the frequency range between the two lowest cuto frequencies.
The cuto frequency for the T E10 (which is the mode with the lowest cuto frequency) is:
q
c 2
f10 =
= 12.5 10
Problem Set 7 Solutions
Problem 7.1
(a)
(i) For an air lled line we know that the propagation velocity is c . Looking at the gure we see the
distance between adjacent voltage minima is A, so the wavelength is = 2A. The frequency of the wave is
given by th
3.012 PS 1
Issued: 09.09.05
Due: 09.20.05
3.012
Fall 05
No plagiarism allowed: see the handbook for students at http:/web.mit.edu/due/handbook.pdf . On
the other hand, you should feel free to consult as much as possible books and other educational
materia